Mr Jennings made the threat in protest at the council's treatment of his children while they were in care. This led the council to seek an emergency injunction against him last week when he was released.
He agreed not to acquire a firearm or carry a weapon in a public place, to visit schools or council offices without prior arrangement and not to assault, threaten, or molest staff, teachers or pupils.
His solicitors reassured the public that he did not possess a firearm, he had never intended to acquire one and he had never intended to cause alarm and anxiety to parents.
Ian Coupe, head of James Wolfe junior school and local secretary of the National Association of Head Teachers, said security had been reviewed in the borough after the Philip Lawrence tragedy. New guidelines were issued at the end of last term.